Algebra Evaluating Expressions Math Workbook 100 Worksheets: Hands-on Practice for Evaluating Algebraic Expressions - Free Printable

Let’s solve each problem one by one, step by step. We’ll substitute the given values into each expression and simplify carefully.

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**Problem 1: Evaluate (a + b)² - (c × d)²
for a = 3, b = 3, c = -2, d = -3**

Step 1: Plug in the numbers
→ (3 + 3)² - ((-2) × (-3))²

Step 2: Simplify inside parentheses
→ (6)² - (6)² [because (-2)×(-3) = 6]

Step 3: Square both
→ 36 - 36

Step 4: Subtract
→ 0

✔ Final Answer for Problem 1: 0

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**Problem 2: Evaluate a + b ÷ c - d
for a = -36, b = 20, c = 4, d = 5**

Remember order of operations: division first!

Step 1: Plug in the numbers
→ -36 + 20 ÷ 4 - 5

Step 2: Do division first → 20 ÷ 4 = 5
→ -36 + 5 - 5

Step 3: Add and subtract left to right
→ (-36 + 5) = -31
→ -31 - 5 = -36

✔ Final Answer for Problem 2: -36

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**Problem 3: Evaluate a - (b + c) ÷ d
for a = 54, b = -36, c = 9, d = -9**

Step 1: Plug in the numbers
→ 54 - ((-36) + 9) ÷ (-9)

Step 2: Simplify inside parentheses → (-36 + 9) = -27
→ 54 - (-27) ÷ (-9)

Step 3: Division next → (-27) ÷ (-9) = 3
→ 54 - 3

Step 4: Subtract → 51

✔ Final Answer for Problem 3: 51

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**Problem 4: Evaluate a + b² ÷ c - d²
for a = 15, b = -10, c = -25, d = -7**

Order of operations: exponents first, then division, then addition/subtraction.

Step 1: Plug in the numbers
→ 15 + (-10)² ÷ (-25) - (-7)²

Step 2: Exponents
→ (-10)² = 100
→ (-7)² = 49
So now: 15 + 100 ÷ (-25) - 49

Step 3: Division → 100 ÷ (-25) = -4
→ 15 + (-4) - 49

Step 4: Left to right
→ 15 - 4 = 11
→ 11 - 49 = -38

✔ Final Answer for Problem 4: -38

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**Problem 5: Evaluate a ÷ b² + c
for a = -81, b = 3, c = 6**

Step 1: Plug in the numbers
→ -81 ÷ (3)² + 6

Step 2: Exponent → 3² = 9
→ -81 ÷ 9 + 6

Step 3: Division → -81 ÷ 9 = -9
→ -9 + 6

Step 4: Addition → -3

✔ Final Answer for Problem 5: -3

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**Problem 6: Evaluate a + [b + (c - d)]²
for a = 12, b = 7, c = 12, d = 18**

Work from innermost parentheses outward.

Step 1: Plug in the numbers
→ 12 + [7 + (12 - 18)]²

Step 2: Innermost parentheses → 12 - 18 = -6
→ 12 + [7 + (-6)]²

Step 3: Inside brackets → 7 + (-6) = 1
→ 12 + (1)²

Step 4: Exponent → 1² = 1
→ 12 + 1

Step 5: Add → 13

✔ Final Answer for Problem 6: 13

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Final Answer:
0, -36, 51, -38, -3, 13